Regular Word automation is not supported when running as a service (including things like ASP.NET). It is a desktop client application with an API to automate that application, not an API to the Word subsystem.
You might try looking at Word Automation Services, but note that this is a SharePoint Server 2010 component.
I would strongly recommend looking at alternatives, such as the various tools (some free, some not) for writing Word documents, or other file formats.
It seems moot, but I also doubt that Word will work on server-core. It is heavily stripped down for scoped server usage, and will be missing many things that a desktop client application will want to use.